• Geophysics and Geophysical Exploration
• /
• v.3 no.1
• /
• pp.13-18
• /
• 2000

We describe the concept of the singularity in the integral equation of electromagnetic (EM) modeling in comparison with that in the integral representation of electric fields in EM theory, which would clarify the singular integral problems of the Green's tensor. We have also derived and classified the singular integrals of the Green's tensors in 3-D, 2.5-D and 2-D as well as in the thin sheet integral equations of the EM scattering problem, which have the most important effect on the accuracy of the numerical solution of the problems.

• East Asian mathematical journal
• /
• v.27 no.1
• /
• pp.51-65
• /
• 2011

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Influence effects of coefficients at lowest derivatives on correctness of studied problems are detected.

• The Journal of the Acoustical Society of Korea
• /
• v.27 no.8
• /
• pp.411-417
• /
• 2008

An alternative formulation of the Helmholtz integral equation derived to express the pressure field explicitly in terms of the velocity vector of a radiating surface is used to solve acoustic radiation and fluid/structure interaction problems. This formulation, derived for arbitrary sources, is similar in form to the Rayleigh's formula for planar sources. Because the surface pressure field is expressed explicitly as a surface integral of the surface velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use BEM to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the non-uniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated for some simple geometries.

• Journal of KSNVE
• /
• v.7 no.6
• /
• pp.975-984
• /
• 1997

A direct boundary element method (DBEM) is developed for thin bodies whose surfaces are rigid or compliant. The Helmholtz integral equation and its normal derivative integral equation are adoped simultaneously to calculate the pressure on both sides of the thin body, instead of the jump values across it, to account for the different surface conditions of each side. Unlike the usual assumption, the normal velocity is assumed to be discontinuous across the thin body. In this approach, only the neutral surface of the thin body has to be discretized. The method is validated by comparison with analytic and/or numerical results for acoustic scattering and radiation from several surface conditions of the thin body; the surfaces are rigid when stationary or vibrating, and part of the interior surface is lined with a sound-absoring material.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.10 no.5
• /
• pp.787-797
• /
• 1986

An implicit approach is employed to obtain a general boundary integral formulation of axisymmetric elastic problems in terms of a pair of singular integral equations. The corresponding kernel functions from the solutions of Navier's equation are derived by applying a three dimensional integral and a direct axisymmetrical approach. A numerical discretization schem including the evaluation of Cauchy principal values of the singular integral is described. Finally the typical axisymmetric elastic models are analyzed, i.e. the hollow sphere, the constant thickness and the V-notched round bar.

• The Pure and Applied Mathematics
• /
• v.24 no.3
• /
• pp.155-169
• /
• 2017

In this paper we obtain some integral inequalities involving impulses and apply our results to a certain integro-differential equation with impulses. First, we obtain a bound of the equation, and we use the bound to study some qualitative properties of the equation.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.12
• /
• pp.3219-3226
• /
• 1994

A model is constructed to evaluate the stress intensity factors for a center crack subjected to polynomial anti-symmetric loading in a layered material. A Fredholm integral equation is derived by Fourier integral transform method. The integral equation is numerically analyzed to evaluate the effects of the ratios of shear modulus, Poisson's ratio and crack length to layer thickness as well as the number of layers on the stress intensity factor. The stress intensity factors are approached to constant values as the number of layers increase and decrease as the polynomial power of the loading increase. In case of the E-glass/Epoxy composite, dimensionless stress intensity factor is affected by cracked-resin layer thickness.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.6
• /
• pp.1382-1387
• /
• 1994

A model is constructed to evaluate the stress intensity factors for a center crack subjected to anti-symmetric loading in a layered material. A Fredholm integral equation is derived using the Fourier integral transform method. The integral equation is numerically analyzed to evaluate the effects of stress intensity factor on the shear modulus, Poisson's ratio and crack length to layer thickness. In case of the isotropic homogeneous material, the values of stress intensity factor derived in the present study agree with the previous solutions.

• Journal of Ocean Engineering and Technology
• /
• v.14 no.2
• /
• pp.1-6
• /
• 2000

Wave energy absorption by a flap equipped with a harbor in a water of finite depth is studied. The wave potential is calculated by a hybrid integral equation consisting of Green integral equations associated with Rankine and Kelvin Green functions. The absorbed wave energy is calculated by both the near-field and far-field methods. The present methods can be used for the design of a flap-harbor wave energy absorber since the numerical results by the two methods are in good agreement.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11b
• /
• pp.1078-1082
• /
• 2001

An alternative formulation of the Helmholtz integral equation is derived to express the pressure field explicitly in terms of the velocity vector of a radiating surface. This formulation, derived for arbitrary sources, is similar in form to the Rayleigh's formula for planar sources. Because the pressure field is expressed explicitly as a surface integral of the particle velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use Boundary element method to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the non-uniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated for some simple geometries.